Methods and apparatuses for quadrature amplitude modulation optimized for phase noise

ABSTRACT

Methods and apparatus for facilitating wireless communication using digital Quadrature Amplitude Modulation are disclosed. A wireless communication device utilizes a signal constellation for quadrature modulating a signal for transmission or quadrature demodulating a received signal. The signal constellation includes multiple constellation symbols and associated bit sequences, which can be translated there between. Specific signal constellations are disclosed.

RELATED APPLICATIONS

This Application is a continuation of PCT/CN2017/091512 filed Jul. 3, 2017, the entirety of which is incorporated herein by reference.

TECHNICAL FIELD

Example embodiments generally relate to the technical field of wireless communications, and in particular to methods and apparatuses for performing quadrature amplitude modulation, using particular quadrature amplitude modulation constellations.

BACKGROUND

Quadrature amplitude modulation (QAM) has found extensive applications in wired and wireless digital communications systems. In a digital QAM scheme, the QAM constellations are specified by both their amplitude and phase in a quadrature coordination. Phase-shift keying (PSK) modulation can be considered as a special case of QAM where the amplitude of a PSK modulation scheme is constant and the PSK constellations are equally spaced on a circle.

The aim of digital QAM is to communicate a message from a transmitter to a receiver. However, such communication must contend with the presence of noise, such as thermal noise and phase noise, as well as other limitations such as transmitter power limitations. Phase noise (frequency offset) is particularly problematic at higher frequencies, such as 60 GHz and above, and can be generated due to imperfect oscillators in both transmitter and receiver. Use of higher-order QAM in the presence of thermal noise, phase noise, and other limitations, can result in unacceptably high error rates, particularly for higher-frequency communication systems.

It may be advantageous to provide a method and apparatus for quadrature amplitude modulation that obviates or mitigates one or more limitations of the prior art.

This background information is provided to reveal information believed by the applicant to be of possible relevance. No admission is necessarily intended, nor should be construed, that any of the preceding information constitutes prior art.

SUMMARY

An object of at least some example embodiments is to provide a method and apparatus for quadrature signal modulation in a wireless communication system.

In accordance with an example embodiment, there is provided a method for wireless communication using digital Quadrature Amplitude Modulation, the method comprising: translating between constellation symbols and bit sequences corresponding to the constellation symbols using a controller of a wireless communication device, in accordance with a 64-point constellation, the constellation symbols used in modulating a signal for transmission or detected in a received signal, or both. Each of the constellation symbols is specified in a row of an example specified table (or specified tables) in accordance with example embodiments, normalized magnitudes of in-phase components of the constellation symbols are specified in one of the “X” and “Y” columns (e.g., first coordinate and second coordinate, respectively) of said one of the tables and normalized magnitudes of quadrature components of the constellation symbols are specified to a in a different one of the “X” and “Y” columns of said one of the tables. Optionally, in any of the preceding embodiments, the signal constellation is specified by the values in the tables as rounded or truncated to three, four, five or six decimal places. Optionally, in any of the preceding embodiments, the signal constellation may be selected from one of a plurality of tables. Optionally, in any of the preceding embodiments, the particular bit sequences associated with the constellation symbols are as listed in the tables, or are derived from the bit sequences listed in the tables by adding a constant binary value to the listed bit sequences, by applying consistent bit reordering operation to the listed bit sequences, or both.

In accordance with example embodiments, there is provided an apparatus for a wireless communication device configured for wireless communication using digital Quadrature Amplitude Modulation, the apparatus comprising: a controller configured to translate between bit sequences and corresponding constellation symbols in accordance with a signal constellation having a specified number of constellation points, the constellation symbols used in modulating a signal for transmission or detected in a received signal, or both. Each of the constellation symbols is specified in a row of an example specified table (or specified tables) in accordance with example embodiments, normalized magnitudes of in-phase components of the constellation symbols are specified in one of the “X” and “Y” columns of said one of the tables and normalized magnitudes of quadrature components of the constellation symbols are specified to a in a different one of the “X” and “Y” columns of said one of the tables. In some embodiments, the signal constellation is specified by the values in the tables as rounded or truncated to three, four, five or six decimal places. Optionally, in any of the preceding embodiments, the signal constellation may be selected from one of a plurality of the tables. Optionally, in any of the preceding embodiments, the particular bit sequences associated with the constellation symbols are as listed in the tables, or are derived from the bit sequences listed in the tables by adding a constant binary value to the listed bit sequences, by applying consistent bit reordering operation to the listed bit sequences, or both.

Another example embodiment is a method for wireless communication using digital Quadrature Amplitude Modulation (QAM), the method comprising: modulating, using a controller of a wireless communication device, a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received; normalized magnitudes of constellation symbols are defined by coordinate pairs in a specified table or tables. In another example embodiment, the method further includes transmitting the modulated signal from the wireless communication device or receiving the signal in the wireless communication device, as applicable. The controller can comprise a modulator or a processor.

Another example embodiment is an apparatus for a wireless communication device configured for wireless communication using digital Quadrature Amplitude Modulation (QAM), the apparatus comprising: a controller configured to modulate a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received. Normalized magnitudes of constellation symbols are defined by coordinate pairs in a specified table or tables. In another example embodiment, the controller is further configured to transmit the modulated signal from the wireless communication device or receive the signal in the wireless communication device, as applicable. The controller can comprise a modulator or a processor.

Another example embodiment is a non-transitory computer readable medium containing instructions for wireless communication using digital Quadrature Amplitude Modulation (QAM), the non-transitory computer readable medium comprising instructions executable by a controller of a wireless communication device, the instructions comprising instructions for performing described methods and functions of apparatuses described herein.

Optionally, in any of the preceding embodiments, the 64-point constellation is a reflection-symmetric constellation.

Optionally, in any of the preceding embodiments, the first coordinates of the coordinate pairs represent normalized magnitudes of one of: in-phase components and quadrature components of the constellation symbols, and the second coordinates of the coordinate pairs represent normalized magnitudes of the other one of the in-phase components and the quadrature components of the constellation symbols.

Optionally, in any of the preceding embodiments, the bit sequences are assigned to the constellation symbols using Gray mapping.

Optionally, in any of the preceding embodiments, each of the bit sequences is of length 6 bits, including 4 quadrant non-specific bits, and wherein, for an index value k ranging from k=1 to k=16 inclusive: the quadrant non-specific bits of the bit sequence corresponding to the constellation symbol defined by a k^(th)-listed one of the coordinate pairs are equal to: a binary representation of k−1; the binary representation of k−1 added to a constant value under Modulo-16 addition; the binary representation of k−1 subjected to a consistent bit reordering, or the binary representation of k−1 added to a constant value under Modulo-16 addition and subjected to the consistent bit reordering.

Optionally, in any of the preceding embodiments, the 64-point constellation is a reflection symmetric constellation, and wherein bit sequences corresponding to constellation symbols within a common group of reflection symmetric constellation symbols have identical quadrant non-specific bits.

Optionally, in any of the preceding embodiments, the controller comprises a mapping module electronic component for said translating.

BRIEF DESCRIPTION OF THE FIGURES

Embodiments will now be described by way of examples with reference to the accompanying drawings, in which like reference numerals may be used to indicate similar features, and in which:

FIG. 1 illustrates a wireless transmitter communication apparatus in accordance with an example embodiment.

FIG. 2 illustrates a wireless receiver communication apparatus in accordance with another example embodiment.

FIG. 3 illustrates a method for wireless transmission of QAM symbols, in accordance with an example embodiment.

FIG. 4 illustrates a method for wireless reception of QAM symbols, in accordance with an example embodiment.

FIG. 5 illustrates a mapping module electronic component in accordance with example embodiments.

FIG. 6 illustrates the generation of a physical layer protocol data unit (PPDU) from a physical layer service data unit (PSDU) in a single carrier physical layer, in accordance with an IEEE 802.11ad wireless communication approach which may be utilized in example embodiments.

FIG. 7 illustrates an IEEE 802.11ad single carrier physical layer frame format and associated block structure which may be utilized in accordance with example embodiments.

FIG. 8 illustrates power spectral density of phase noise for IEEE 802.11ad.

FIG. 9 illustrates a 64-point signal constellation for QAM in accordance with an example embodiment.

FIG. 10 illustrates a 64-point signal constellation for QAM in accordance with another example embodiment.

FIG. 11 illustrates a first example performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR), in accordance with an example embodiment.

FIG. 12 illustrates a second example performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR), in accordance with an example embodiment.

FIG. 13 illustrates a third example performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR), in accordance with an example embodiment.

FIG. 14 illustrates a fourth example performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR), in accordance with an example embodiment.

FIG. 15 illustrates the standard deviation of residual phase noise vs. SNR (Signal-To-Noise Ratio) using a linear interpolation phase noise mitigation method in accordance with an example embodiment.

FIG. 16 illustrates transmitter and receiver systems in accordance with an example embodiment.

FIG. 17 illustrates a simplified soft limiter for enforcing a peak power constraint, in accordance with an example embodiment.

FIG. 18 illustrates a constellation optimization procedure according to an example embodiment.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

Example embodiments are generally directed to a method and apparatus for wireless communication using a digital QAM signal constellation as described herein. The method includes modulating and/or demodulating a signal according to the described constellation, using a wireless transmitter and/or receiver, or associated signal processing electronics. The apparatus includes a wireless transmitter and/or receiver, or associated signal processing electronics, configured to modulate and/or demodulate a signal according to the described constellation. As used herein, QAM refers generally to any amplitude modulation which includes an in-phase component and a quadrature component, for modulating two carrier signals which are in quadrature with each other. For example, phase-shift keying is regarded as a particular form of QAM.

Example embodiments may be used to wirelessly communicate information between a transmitter and receiver. The information can include control plane data, application data, or user messaging data, for example. On the transmitter side, the information is initially represented as a plurality of binary digits (bits), and modulating the signal comprises mapping a given number m of bits at a time to a corresponding symbol in the signal constellation. On the receiver side, the information is represented via a quadrature modulated waveform, and demodulating the signal comprises mapping portions of the waveform corresponding to a symbol in the signal constellation to an associated sequence of m bits.

Example embodiments apply high order modulation schemes, in which each of M=2^(m) symbols in a QAM modulation represents multiple (m>1) bits. Table 1 shows the spectral efficiency r=mr_(c) and required minimum Signal to Noise Ratio (SNR) based on the Shannon capacity limit, corresponding to different code rates r_(c) and to different cardinalities of constellation sets M=2^(m), m=2, . . . , 8.

TABLE 1 m 2 3 4 5 6 7 8 min min min min min min min r SNR r SNR r SNR r SNR r SNR r SNR r SNR r_(c) 1/2 1.00 0.0 1.50 2.6 2.00 4.8 2.50 6.7 3.00 8.5 3.50 10.1 4.00 11.8 5/8 1.25 1.4 1.88 4.3 2.50 6.7 3.13 8.9 3.75 11.0 4.38 13.0 5.00 14.9 3/4 1.50 2.6 2.25 5.7 3.00 8.5 3.75 11.0 4.50 13.4 5.25 15.7 6.00 18.0 7/8 1.75 3.7 2.63 7.1 3.50 10.1 4.38 13.0 5.25 15.7 6.13 18.4 7.00 21.0

In accordance with example embodiments, and with reference to FIG. 1, a wireless communication apparatus or device comprising an input interface 110, a transmitter mapping module 120, and a transmitter module 130 is disclosed. The input interface 110 is configured to receive data to be wirelessly transmitted. The data may be represented in binary, and may include at least m bits, where m is the base-2 logarithm of the modulation order of the quadrature modulation constellation being used. The transmitter mapping module 120 is configured to receive one or more bit sequences. Each bit sequence is representative of a portion of the data of length m. A bit sequence may correspond directly to m contiguous bits of the data, or it may be derived from the data by applying operations such as scrambling, interleaving, channel coding, etc. The transmitter mapping module is further configured to generate, for each bit sequence, a corresponding constellation symbol 122 having an in-phase component 124 and a quadrature component 126. Correspondence between a bit sequence and the generated constellation symbol is given according to a particular signal constellation 128, as described herein. Typically, multiple bit sequences representative of the input data are used to generate a sequence of constellation symbols. The transmitter module 130 is configured to generate and transmit a wireless signal 135 based on the constellation symbols generated by the mapping module. The transmitter module 130 can comprise or be operably coupled with an associated antenna, and/or further signal processing components. A modulator or controller of the wireless communication apparatus can be used to perform the modulation.

Generation of wireless signals based on constellation symbols can be performed in a manner as would be readily understood by a worker skilled in the art. For example, a sequence of in-phase components can be used to amplitude modulate a first sinusoidal carrier signal, and a corresponding sequence of quadrature components can be used to amplitude modulate a second sinusoidal carrier signal that is out of phase (in quadrature) with the first sinusoidal signal. The sequences of in-phase and quadrature components can be represented, for example, as pulse trains or other electrical signals with amplitudes varying according to the magnitudes of the in-phase and quadrature components, for example, to be used for amplitude modulation of the carrier signals. The amplitude modulated carrier signals are then added together and transmitted.

In accordance with an example embodiment, and with reference to FIG. 2, a wireless communication apparatus comprising a receiver module 210, a receiver mapping module 220, and an output interface 230 is disclosed. The receiver module is configured to receive a wireless signal 212 and, in an example embodiment that implements hard-decision decoding, generate constellation symbols 214 based on the wireless signal, each constellation symbol having an in-phase component 216 and a quadrature component 218. Generation of constellation symbols based on a received wireless signal can be performed in a manner as would be readily understood by a worker skilled in the art. For example, the received signal can be multiplied by locally generated copies of the carrier signal, low-pass filtering may be applied to the result, and the output of the low-pass filtering can be sampled to recover representations of the in-phase and quadrature components of the constellation symbols. The sampling includes quantization. For hard-decision decoding, in an example embodiment, the receiver mapping module 220 is configured to receive constellation symbols 214 and generate, for each constellation symbol, a bit sequence 228 corresponding to the constellation symbol. Correspondence between a bit sequence and a received constellation symbol is given according to a particular signal constellation 226, as described herein. The output interface 230 is configured to provide data 238, a portion of the data represented by the generated bit sequence 228 associated with a received constellation symbol. Alternatively, in another example embodiment, soft-decision decoding, such as Low Density Parity Check LDPC decoding or turbo decoding may be employed, in which a demodulator outputs a sequence of log-likelihood ratios (LLRs) rather than performing direct symbol-to-bit mapping. A decoder then uses the LLR values for decoding. Note that “modulating” herein not only refers to QAM modulating and/or generating of a signal, but can also be used to refer to decoding or demodulating of the received signal, because modulating is being performed in both cases. The receiver module 210 can comprise or be operably coupled with an associated antenna, and/or further signal processing components.

The provided group of m bits may directly represent m bits of the data, or the portion of data may be obtained at least partially from the generated bit sequence by applying operations such as descrambling, deinterleaving, decoding, etc. Typically, for hard-decision decoding in an example embodiment, the received wireless signal is used to generate a sequence of constellation symbols which are passed to the receiver mapping module. The receiver mapping module then generates the data using hard-decision decoding or soft-decision decoding.

In accordance with example embodiments, and with reference to FIG. 3, there is provided a method for facilitating wireless transmission of QAM symbols. The method includes receiving 310, via an internal input interface of a wireless communication device, data to be wirelessly transmitted. The data may include at least m bits, where m is determined by the modulation order of the quadrature modulation scheme being used. The method further includes providing 320 one or more bit sequences. Each bit sequence is representative of a portion of the data, for example subsequent to operations such as but not necessarily limited to channel coding. Each bit sequence is of length m, where m is the predetermined value corresponding to the modulation order. The method further includes determining 330, for each bit sequence, a corresponding constellation symbol having an in-phase component and a quadrature component. Correspondence between a bit sequence and the provided constellation symbol is given according to a particular signal constellation, as described herein. Typically, multiple bit sequences representative of the input data are used to generate a sequence of constellation symbols. The method may further include generating and transmitting 340 a wireless signal based on the determined constellation symbols. The generation of the wireless signal comprises modulating a carrier signal according to the generated sequence of constellation symbols.

In accordance with an example embodiment, and with reference to FIG. 4, there is provided a method for performing wireless reception and demodulation of QAM symbols. A modulator or controller of the wireless communication apparatus can be used to perform the demodulation. The method includes receiving 410 a wireless signal and, in an example embodiment that implements hard-decision decoding, generating 420 received baseband symbols based on the wireless signal, each received baseband symbol having an in-phase component and a quadrature component. The received baseband symbol can either generate a bit sequence by mapping the most likely constellation symbol to a corresponding bit sequence based on the constellation mapping (as in hard-decision decoding), or form a sequence of bit-related soft values indicating the likelihood of bit values at the specific bit positions of a bit sequence corresponding to the selected constellation symbol (as in soft-decision decoding). As such, the method further includes providing 430 bit sequences or soft values corresponding to the received baseband symbol. A received constellation symbol is given according to a particular signal constellation, as described herein. The method further includes providing 440 data, a portion of the data represented by the provided bit sequence or a sequence of soft values associated with a received symbol. The data may be provided, for example, by performing channel decoding and other operations on the bit sequences.

Example embodiments generally provide for methods and apparatus for generating constellation symbols based on bit sequences and/or generating bit sequences or sequences of bit-related soft values based on constellation symbols, according to a correspondence which is specified by a signal constellation as described herein. Such embodiments may be represented in the transmitter mapping module and receiver mapping module described above, collectively referred to as mapping modules. For example, a provided apparatus may receive groups of m bits and generate constellation symbols, including in-phase and quadrature components, corresponding to the received bit sequences. Bit sequences may be represented by digital signals, such as serial or parallel digital data signals, for example. Sequences of constellation symbols may be represented, for example, by pairs of electrical signals having amplitudes which vary with the magnitudes of the in-phase and quadrature components of the constellation symbols. As another example, sequences of constellation symbols may be represented by time-varying digital or analog signals which convey instructions for use by another electronic device to generate such pairs of electrical signals. For a reception operation, a provided apparatus may receive pairs of electrical signals having amplitudes or other characteristics which are interpreted, by the apparatus, as the magnitudes of a received sequence of in-phase and quadrature components of a received sequence of constellation symbols. The apparatus may then generate a plurality of bit sequences or plurality of bit-related soft values in a larger sequence, which correspond to the received sequence of constellation symbols.

Example embodiments therefore comprise translating, for example using mapping modules, between constellation symbols and bit sequences according to a particular signal constellation. In the case of signal transmission, the translating includes generating constellation symbols based on bit sequences. In the case of signal reception, the translating includes generating bit sequences or bit-related sequences of soft values based on constellation symbols. Other aspects of signal modulation and/or demodulation, such as varying the amplitudes of carrier signals and/or processing a received signal recover constellation symbols, may be, but are not necessarily, included in example embodiments. Translating can therefore refer to modulating a signal for transmission, or demodulating a signal that is received.

FIG. 5 illustrates a mapping module electronic component 500 provided in accordance with example embodiments. The electronic component may be provided as a semiconductor circuit, for example forming part or all of an integrated circuit package. The mapping module electronic component can be configured as a transmitter mapping module, a receiver mapping module, or both. The mapping module includes a first interface 510 configured to provide and/or receive groups of m bits. The mapping module further includes a second interface 520 configured to receive and/or provide signals indicative of constellation symbols. In some embodiments the second interface may include a first terminal 522 for receiving and/or providing in-phase components of the constellation symbols, and a second terminal 524 for receiving and/or providing quadrature components of the constellation symbols. The mapping module is configured to translate, via translation circuitry 530, between bit sequences and constellation symbols according to a signal constellation 535. The translation circuitry may be digital or analog circuitry. In some embodiments, the translation circuitry is preconfigured according to a certain signal constellation. In other embodiments, the translation circuitry is reconfigurable according to a signal constellation which can be specified or selected via a control interface 540 of the mapping module.

Example embodiments are applied for signal modulation in millimeter wave (mmWave) wireless communication systems. Some example embodiments are applicable to signal modulation in communication systems, as specified in the IEEE 802.11 series of standards. Some example embodiments are applicable to signal modulation in wireless communication systems employing a carrier frequency around 60 GHz. It will be readily appreciated that example embodiments may be applied to other wireless communication systems, as well as to wired or optical systems, and in other communication environments.

FIG. 6 illustrates the generation of a physical layer protocol data unit (PPDU) from a physical layer service data unit (PSDU) in a single carrier physical layer, in accordance with a wireless communication approach which may be utilized in example embodiments. The operations illustrated in FIG. 6 are comparable to those specified in the IEEE 802.11ad wireless local area network protocol, and details can be found in the IEEE 802.11ad-2012 standards document, published December, 2012 and having E-ISBN 978-0-7381-8096-0. The single carrier physical layer may employ low-density parity check (LDPC) codes, for example with a code word length of 672. The input PSDU data 605 undergoes scrambling 610, and the scrambled bits are fragmented 615 to provide input bits 617. The input bits are then encoded 620, for example using a LDPC code, to provide coded bits 622. An optional interleaving operation 623 can be performed following encoding. Interleaving can include shuffling encoded bits, for example. The coded and possibly interleaved bits then optionally undergo zero padding 625. The coded bits, with or without zero padding, are then modulated 630. In example embodiments, modulation may be performed using a signal constellation as described herein. The modulated symbols 632 then undergo symbol blocking and guard insertion 635, thereby providing the PPDU 640. In general, modulation operations according to example embodiments may be performed after channel coding, such as LDPC coding.

FIG. 7 illustrates an IEEE 802.11ad single carrier physical layer frame format 700 and associated block structure which may be utilized in accordance with example embodiments. A set of three contiguous data block structures 750 a, 750 b, 750 c are illustrated in detail. The number of data block structures can be variable. Each data block structure 750 a, 750 b, 750 c in a PPDU includes 448 modulated data symbols 752 preceded by a guard interval (GI) 755. For multiple contiguous blocks, groups of 448 modulated data symbols 752 are thus separated by GIs 755 of the same length-64 bipolar Golay sequence. The two GIs 755 preceding and following a given group of 448 modulated data symbols 752 form a cyclic prefix permitting FFT/IFFT operations at a receiver to perform frequency-domain equalization. In addition, the known GIs can be used for other purposes such as phase noise estimation for mitigation of phase noise.

Example embodiments relate to signal modulation and/or demodulation in single carrier systems, for example using the data block structure as illustrated in FIG. 7. Example embodiments relate to signal modulation and/or demodulation in single carrier systems with other formats of data block structure.

Example embodiments relate to signal modulation and/or demodulation in communication systems with or without phase noise. Phase noise can significantly degrade the link performance in high-frequency communication systems employing high order digital QAM modulations. The power spectral density of one model of phase noise considered for IEEE 802.11ad is shown in Eq. (1):

$\begin{matrix} {{{PSD}(f)} = {{{{PSD}(0)}\left\lbrack \frac{1 + \left( {f/f_{z}} \right)^{2}}{1 + \left( {f/f_{p}} \right)^{2}} \right\rbrack}.}} & (1) \end{matrix}$

The parameterization of this model as considered for IEEE 802.11ad is such that: PSD(0)=−90 dBc/Hz; Pole frequency f_(p)=1 MHz; Zero frequency f_(z)=100 MHz; Corresponding PSD(infinity)=−130 dBc/Hz; and impairment is modeled at both transmitter and receiver. In example embodiments, signal constellations are provided which have been configured in view of the above phase noise model.

FIG. 8 illustrates power spectral density of phase noise for IEEE 802.11ad for this model.

Example embodiments include signal constellations which have been generated according to a constellation optimization in view of both the transmit power and phase noise constraints. In some example embodiments the phase noise model and the PA model used for the constellation optimization are given in Equations (1) and FIG. 17. Multiple sets of 64-point constellations may be generated using this optimization approach. Selected ones of these constellations are disclosed herein.

It is noted that a constellation that is considered optimal for a particular code rate is not limited for use with that code rate. Rather, a constellation can be used for various code rates, even if it has been optimized for use with a particular code rate. The use of the constellation for different code rates may result in a reduction in performance and/or loss of optimality. More generally, it is noted that a constellation that is considered optimal for a particular set of conditions can be used in other conditions, with a possible reduction in performance and/or loss of optimality. However, such a performance reduction may be acceptable. Further, the reduced complexity due to the ability to use the same constellation under different conditions may result in a benefit which offsets the performance reduction.

Various signal constellations provided in accordance with example embodiments are described in detail below. Each signal constellation represents a set of constellation symbols. A signal constellation having M points is referred to as an M-point constellation. In some example embodiments, the x coordinate value of a constellation symbol indicates the (normalized) magnitude of the in-phase component of the constellation symbol, and the y coordinate value of a constellation symbol indicates the (normalized) magnitude of the quadrature component of the constellation symbol. Alternatively, the x coordinate value of a constellation symbol may indicate the (normalized) magnitude of the quadrature component of the constellation symbol, and the y coordinate value of a constellation symbol indicates the (normalized) magnitude of the in-phase component of the constellation symbol. A sequence of m bits may be associated with each constellation symbol.

In some cases, only the first quadrant of a constellation is specified. As such, in some embodiments, the locations of constellation symbols in other quadrants of the constellation can be readily obtained from the constellation symbols in the first quadrant by reflection symmetry. For reflection symmetry, given constellation symbols in the first quadrant, the locations of constellation symbols in the second quadrant can be obtained by reflection in the Y (vertical) axis. More specifically, the reflection operation can include, for each constellation symbol in the first quadrant specified by vector location (x,y), obtaining a constellation symbol in the second quadrant specified by vector location (−x, y). Similarly, given constellation symbols in the first quadrant, the locations of constellation symbol in the third quadrant can be obtained by reflection in the Y axis, followed by reflection in the X (horizontal) axis. More specifically, the reflection operation can include, for each constellation symbol in the first quadrant specified by vector location (x,y), where x and y are non-negative values, obtaining a constellation symbol in the third quadrant specified by vector location (−x,−y). Similarly, given constellation symbols in the first quadrant, the locations of constellation symbol in the fourth quadrant can be obtained by reflection in the X (horizontal) axis. More specifically, the reflection operation can include, for each constellation symbol in the first quadrant specified by vector location (x,y), obtaining a constellation symbol in the second quadrant specified by vector location (x, −y). Alternatively to obtain constellation symbols in different quadrants from those of the first quadrant by the reflection operations above, a series of reflection operations can be used. For example, the constellation symbols in the second quadrant can be obtained from those of the first quadrant by reflection in the Y axis, the constellation symbols in the third quadrant can be obtained from those of the second quadrant by reflection in the X axis, and the constellation symbols in the fourth quadrant can be obtained from those of the third quadrant by reflection in the Y axis. As used herein, the term “reflection symmetric constellation symbols” refers to a set of four constellation symbols (x,y), (x,−y), (−x,−y), (−x,y) for given values of x and y.

As used herein, the term “symmetric constellation symbols” refers to “reflection symmetric constellation symbols”. A constellation consisting of reflection symmetric constellation symbols may also be referred to as a reflection symmetric constellation, or as a “symmetric constellation”.

In another example embodiment, when constellation symbols of a first quadrant are specified, the locations of constellation symbols in other quadrants of the constellation can be obtained from the constellation symbols in the first quadrant by phase rotation.

In some example embodiments, the illustrated signal constellations can be scaled by a nonzero scaling factor k. Scaling of a signal constellation can be performed by mapping each constellation symbol (x,y) in the constellation to a new constellation symbol (kx,ky). The (x,y) coordinate values illustrated in FIGS. 9-10 and specified in Tables 2-3 are nominal. In Tables 2-3 constellation magnitudes are normalized such that the average power, across all constellation symbols, is equal to one. In Tables 2-3, constellation magnitudes are normalized such that the power of each constellation symbol is less than or equal to one. The specified coordinate values may alternatively be normalized such that the peak power, among all constellation symbols, is equal to one. The present description of the specified constellations should be understood to include other scalings or normalizations thereof, for example as would be readily understood by a worker skilled in the art.

In some example embodiments, the (x,y) locations of constellation symbols in the illustrated signal constellations can be varied by a limited amount. For example, when the locations of constellation symbols are specified in one embodiment with a precision of d decimal places, another embodiment may correspond to the same general locations of constellation symbols, but specified with a precision of d−1 decimal places, another embodiment correspond to the same general locations of constellation symbols but specified with a precision of d−2 decimal places, and yet another embodiment correspond to the same general locations of constellation symbols but specified with a precision of d−3 decimal places. The lower precision embodiment can be obtained from the higher precision embodiment through rounding or truncation. In some example embodiments, the normalized (x,y) locations of the constellation symbols can be specified to 3, 4, 5, or 6 decimal places. A magnitude that is defined by a coordinate value to at least d decimal places of precision is a magnitude which, when measured, agrees with the coordinate value to at least d decimal places of precision, further decimal places of the measurement and/or coordinate value being either discarded via truncation or subjected to a rounding operation to the d^(th) decimal place.

In some embodiments, the precision of the decimal places may be related to Error Vector Magnitude (EVM) requirement, taking into account factors such as I/Q arm amplitude and phase balance, DC offset, and phase noise. In IEEE 802.11ad, EVM is typically required to be as low as −21 dB for single carrier transmissions and −26 dB for OFDM transmissions.

As another example, when the locations of constellation symbols are specified in a first embodiment with a precision of d decimal places, a second embodiment may correspond to the same general locations of constellation symbols, but varied by up to 6 units, where 6 is on the order of 10^(−d), or alternatively 10^(−d+1) or 10^(−d+2), so that, for example, given a constellation symbol (x,y) in the first embodiment, the second embodiment may include a corresponding constellation symbol (x′,y′), where (x−δ,y−δ)<(x′,y′)<(x+δ,y+δ), or alternatively where ∥(x′, y′)−(x,y)∥<δ.

In example embodiments, the normalized magnitudes of the constellation symbols are defined by coordinates which fall anywhere within a rectangular region, including along a boundary of the rectangular region. For each constellation symbol, the rectangular region is defined by a first corner specified by a first coordinate pair and a second corner specified by a second coordinate pair. The second corner is diagonally opposite the first corner. For a signal constellation as specified in one of Tables 2-3, and for each listed coordinate pair in the table, the first coordinate pair (specifying the first corner of the rectangular region) can be derived from the listed coordinate pair by rounding down both X and Y values of the listed coordinate pair. The second coordinate pair (specifying the second corner of the rectangular region) can be derived from the listed coordinate pair by rounding up both X and Y values of the listed coordinate pair. In some embodiments, rounding is performed to the nearest thousandth, as would be readily understood by a worker skilled in the art. In some embodiments, rounding is performed to the nearest ten thousandth. In some embodiments, rounding is performed to the nearest hundred thousandth.

As such, for each of original Tables 2-3, a new table can be defined in which the “X” column of the original table is replaced with a pair of columns “Xmin” and “Xmax,” and the “Y” column of the original table is replaced with a pair of columns “Ymin” and “Ymax.” The “Xmin” and “Ymin” columns list the X and Y values of the first coordinate pairs, and the “Xmax” and “Ymax” columns list the X and Y values of the second coordinate pairs. The new table indicates a set of ranges for the constellation symbols, such that the normalized magnitude of each constellation symbol has an X coordinate value lying between a value specified in a corresponding row of the “Xmin” column and a value specified in the same row of the “Xmax” column, and further such that the normalized magnitude of the constellation symbol has a Y coordinate value lying between a value specified in the same row of the “Ymin” column and a value specified in the same row of the “Ymax” column. Such new tables are not explicitly listed in the present disclosure for the sake of brevity, however they can be readily derived as described above by a person skilled in the art.

In some example embodiments, rather than determining the corners of the rectangular regions via rounding, the first corner of the rectangular region can be derived from the listed coordinate pair by subtracting a first predetermined value from the X value of the listed coordinate pair, and subtracting a second predetermined value from the Y value of the listed coordinate pair. The second coordinate pair specifying the second corner of the rectangular region can be derived from the listed coordinate pair by adding the first predetermined value to the X value of the listed coordinate pair, and adding the second predetermined value to the Y value of the listed coordinate pair. The first and second predetermined values can be values which are less than or equal to 0.0005, for example.

In addition to specifying the vector locations of the constellation symbols in the XY plane, example embodiments specify the bit sequences corresponding to each of the constellation symbols. As will be readily understood by a worker skilled in the art, given an input group of m bits, modulation includes identifying a symbol in the signal constellation corresponding to the bit sequence, and modulating a signal according to the identified symbol. Similarly, demodulation of a received signal includes identifying a symbol in the signal constellation most closely corresponding to a given portion of the received signal, and outputting the bit sequence corresponding to the identified symbol or the bit-related sequence of soft values corresponding to the constellation. The correspondence between a signal and a constellation symbol may be such that, where the signal is locally describable by the function A cos(ωt)+B sin(ωt), the corresponding constellation symbol is the closest constellation symbol in the XY plane to point (A,B).

In some example embodiments, each group of m bits includes two quadrant-specifying bits. The quadrant-specifying bits may be at fixed locations in the bit sequence. For example, the first two bits (most significant bits) of a bit sequence may be the quadrant-specifying bits. The remaining m−2 bits of a bit sequence are referred to as quadrant non-specific bits. In some embodiments, the quadrant specifying bits corresponding to all constellation symbols in the first quadrant are 00, the quadrant specifying bits corresponding to all constellation symbols in the second quadrant are 10, the quadrant specifying bits corresponding to all constellation symbols in the third quadrant are 11, and the quadrant specifying bits corresponding to all constellation symbols in the fourth quadrant are 01.

In some example embodiments, the quadrant non-specific bits (for example the m−2 least significant bits) of each given constellation symbol may be identical to the quadrant non-specific bits of each other constellation symbol within the same set of symmetric constellation symbols as the given constellation symbol.

It will be readily understood that the correspondence between bit sequences and constellation symbols can be varied in several ways. For example, each of the illustrated bit values inverted, such that a “0” bit becomes a “1” and vice versa. As another example, the illustrated bit positions can be re-ordered. The reordering may be a consistent bit reordering, i.e. in which the same reordering is applied to all bit sequences in a constellation. A simple example of a reordering is a reversal of all bits, for example such that group abcd is replaced by group dcba. As yet another example, a constant value can be added to each of the illustrated bit sequences using a modulo-M binary addition operation, where M=2^(m) and m is the number of bits in each bit sequence. It is noted that bit inversion corresponds to addition of a particular constant value consisting of all binary ones. A combination of bit reordering and addition of a constant value may also be performed.

In some embodiments, for an index value k ranging from k=1 to k=2^(m−2) inclusive, where m is the number of bits in each bit sequence: the quadrant non-specific bits of the bit sequence corresponding to the constellation symbol defined by a k^(th)-listed one of the coordinate pairs are equal to: a binary representation of k−1; the binary representation of k−1 added to a constant value under Modulo-2^(m−2) addition; the binary representation of k−1 subjected to a consistent bit reordering, or the binary representation of k−1 added to a constant value under Modulo-2^(m−2) addition and subjected to the consistent bit reordering.

In an example embodiment, m=6, for 16 constellation symbols per quadrant in a 64-point constellation.

It is noted that, in Tables 2-3, the bit sequences associated with the constellation symbols correspond to binary representations of the position of the constellation symbol in the list. For example, the first-listed constellation symbol is associated with bit sequence ‘0 . . . 000’, the second-listed constellation symbol is associated with bit sequence ‘0 . . . 001’, etc.

In some example embodiments, bit sequences are assigned to constellation symbols using a Gray mapping. Gray mapping comprises associating bit patterns (bit sequences) with constellation symbols, such that the bit sequences associated with adjacent constellation symbols differ by only one bit. That is, the bit sequences assigned to the constellation symbols closest to a first constellation symbol differ by one bit from the bit sequence assigned to the first constellation symbol. Two dimensional Gray mapping comprises associating bit sequences with constellation symbols, such that the bit sequences associated with adjacent constellation symbols differ by only one bit, and the bit sequences associated with the next nearest constellation symbols differ by two bits. The term “adjacent” can be taken to mean closest in terms of a distance metric applied to constellation points in the signal constellation.

FIG. 9 illustrates a 64-point signal constellation 900 provided in accordance with an example embodiment. The corresponding (x,y) coordinate values of the constellation symbols illustrated in FIG. 9 are provided to six decimal places in Table 2. The signal constellation 900 of FIG. 9 is optimized for use with a code rate R_(C) of 5/6, and phase noise standard deviation (PN STD) equal to 7 degrees after Phase Noise (PN) mitigation. The constellation 900 is also suitable for use with other code rates, in an example embodiment. The code rate corresponds to a channel code which is applied to the bit sequences prior to mapping to constellation symbols for transmission, and which is used for decoding to recover the coded information bits. In FIGS. 9-10, bit sequences (according to some example embodiments) are shown generally above their corresponding constellation points. Ambiguities can be resolved by reference to the corresponding tables.

FIG. 10 illustrates a 64-point signal constellation 950 provided in accordance with another example embodiment. The corresponding (x,y) coordinate values of the constellation symbols illustrated in FIG. 10 are provided to six decimal places in Table 3. The signal constellation 950 of FIG. 10 is optimized for use with a code rate R_(C) of 7/8, phase noise standard deviation (PN STD) equal to 4 degrees after Phase Noise (PN) mitigation. The constellation 950 is also suitable for use with other code rates, in an example embodiment.

The constellations described above with respect to FIGS. 9-10 and Tables 2-3 were initially derived by an optimization operation which produced signal constellations which were believed to be optimal for single carrier scenarios exhibiting both phase noise and power amplifier nonlinearity impairments. However, the constellations are not necessarily limited to use in such scenarios.

The (x,y) coordinate values provided in Tables 2-3 are specified to a level of precision of six decimal places. In some embodiments, the coordinate values of the constellation symbols illustrated in FIGS. 9-10 and shown in Tables 2-3 can be truncated to a level of precision of three, four, or five decimal places. In another example embodiment, the coordinate values of the constellation symbols illustrated in FIGS. 9-10 and shown in Tables 2-3 can be rounded to a level of precision of three, four, or five decimal places.

Example embodiments provide for a method and apparatus for performing wireless communication using digital Quadrature Amplitude Modulation. The method and apparatus involve utilizing, by a mapping module electronic component of a wireless communication device, a signal constellation for modulating a signal for transmission or demodulating a received signal, the signal constellation comprising a plurality of constellation symbols. The signal constellation may be obtained using an optimization procedure for example as described below. It is noted that the optimization procedure below is not intended to limit the disclosed signal constellations. Rather, the optimization procedure is provided as an example of how these and similar constellations may be obtained, and the circumstances under which they may be expected to perform well.

In a practical system, phase noise may be said to have a memory. That is, the state of the phase noise at a given time may depend on the state of the phase noise at previous times. As such, according to example embodiments, the residual phase error caused by the imperfect cancellation for phase noise with memory is obtained based on the specified pilot distribution and the methods for phase estimation and phase noise mitigation. The residual phase error is assumed to be a white random process after phase noise mitigation. Therefore, with the aid of transformation of phase noise with memory to the memoryless residual phase error, methods for constellation optimization with white phase noise constraint and white Gaussian noise can be applied to constellation optimization in the presence of a constraint representing phase noise with memory.

According to an example embodiment, a simple and efficient algorithm for the estimation of the phase noise based on the presence of a pilot field of length L every W transmitted symbols, with a pilot overhead OH=L/W may be utilized. The output of the channel affected by the phase noise θ_(k) and thermal noise n_(k) may be written as: r _(k) =e ^(jθ) ^(k) p _(k) +n _(k)

If the known pilot symbols are placed in contiguous positions k∈[nW−L/2,nW+L/2], with arbitrary integer n, a phase estimate corresponding to the middle of the pilot field can be calculated as follows:

$\begin{matrix} {{\hat{\theta}}_{nW} = {{\tan^{- 1}\left( \frac{\sum\limits_{k = {{nW} - {L/2}}}^{{nW} + {L/2} - 1}{\left( {r_{k}p_{k}^{*}} \right)}}{\sum\limits_{k = {{nW} - {L/2}}}^{{nW} + {L/2} - 1}{\left( {r_{k}p_{k}^{*}} \right)}} \right)}.}} & (4) \end{matrix}$

To derive a sequence of phases between two consecutive phase estimates calculated using Equation (4), that is the (nW)^(th) and ((n+1)W)^(th) phase estimates, the following linear interpolation formula is used:

$\begin{matrix} {{{\hat{\theta}}_{{nW} + m} = {{{\left\lbrack \frac{W - m}{W} \right\rbrack{\hat{\theta}}_{nW}} + {\left\lbrack \frac{m}{W} \right\rbrack{\hat{\theta}}_{{({n + 1})}W}m}} = 1}},\ldots\mspace{11mu},{W - 1.}} & (5) \end{matrix}$

For a given overhead OH=L/W, the optimal length of the pilot field L can be obtained by trading off accuracy of the estimation Equation (4) versus accuracy of interpolation Equation (5). As shown in FIG. 7, in an IEEE 802.11ad Single Carrier (SC) block, the pilot field length L=64 and the single SC block length W=512. Therefore, OH=64/512=12.5%.

Another example phase noise mitigation algorithm can improve the phase estimate between two pilot insertions using a data-aided phase-locked loop (PLL) of first order. In example embodiments, both linear interpolation and PLL in the receiver can be implemented.

After mitigation of phase noise, the power spectral density (PSD) of the residual phase error is assumed to be white. Standard deviation of residual phase noise σ_(φ) is used to evaluate the phase errors after a phase noise mitigation process and is used to optimize the constellations. FIG. 15 shows the standard deviation of residual phase noise vs. SNR using the linear interpolation phase noise mitigation method (5). The standard deviation of the residual phase noise (left vertical axis) versus SNR for a system baud rate R_(s)=2 GHz, and a pilot overhead of 12.5% is shown. The solid line curve corresponds to the 802.11ad SC frame structure (L=64, W=512). The dashed curve corresponds to the optimal pilot distribution. The dotted curve shows the optimal pilot field length (to be read in the right vertical axis).

Performance of a given signal constellation over a channel under ideal detection and decoding can be computed using the Mutual Information (MI):

$\begin{matrix} {{MI} = {E\left\lbrack {\log\;\frac{P\left( {Z❘W} \right)}{P(Z)}} \right\rbrack}} & (6) \end{matrix}$

or using the Pragmatic Mutual Information (PMI):

$\begin{matrix} {{PMI} = {\sum\limits_{i = 1}^{m}{{E\left\lbrack {\log\;\frac{P\left( {Z❘E_{i}} \right)}{P(Z)}} \right\rbrack}.}}} & (7) \end{matrix}$

FIG. 16 illustrates transmitter and receiver systems bounded by the PMI. In the FIG. 16 as well as the above Equations (6) and (7), W and Z represent the input and output of channel respectively and B_(i) is the i^(th) bit in W. The MI provides an upper bound on the maximum spectral efficiency, defined as r=mr_(c), where m is the number of bits associated to each modulation symbol and r_(c) is the binary code rate. However, in practical systems optimization of signal constellations is performed under the PMI approach. To improve the performance of pragmatic systems, the mapping of bits to constellation can be suitably optimized, for example using Gray mapping. Although the PMI can be in general quite different from the MI, the difference can be reduced significantly when using optimized constellations and bit-to-signal mappings.

The computation of PMI can be performed with numerical techniques when the conditional distribution of the channel P(Z|W) is known. When the channel is memoryless, the output at a given time instant only depends on the corresponding input at the same time and the computation of PMI becomes easier. Practical memoryless channel models include AWGN and White phase noise channels.

In channels constrained by the use of a nonlinear amplifier the optimization of the constellation may be appropriately modified. In these cases, the AM/AM curve of the nonlinearity may be represented using the simplified soft limiter shown FIG. 17 by enforcing a peak power constraint. Peak power of the constellation may then become a relevant parameter.

The following system conditions were used in the computation of signal constellations according to an example optimization procedure. Signal constellations with 64 modulation points were considered. Five code rates: r_(c)=½, ⅝, ¾, 13/16, ⅞ were considered. Channel scenarios was considered corresponding to AWGN with non linearity and residual phase noise corresponding to the standard (64/512) pilot distribution. The non linearity is represented using a Peak Signal-to-Noise ratio (PSNR) constraint.

According to example embodiments, for each pair of code rate and constellation size, as well as for various levels of the residual phase noise, a constellation and the corresponding binary labeling are designed to achieve a PMI larger than the target spectral efficiency r=mr_(c) with the minimum possible SNR or PSNR.

Given modulation format, code rate and channel scenario, constellation and bit sequence labeling can be optimized to minimize SNR to achieve a PMI greater than the target spectral efficiency r=mr_(c). FIG. 18 illustrates an applicable constellation optimization procedure using a simulated annealing (SA) technique, according to an example embodiment. Example embodiments involve providing a signal constellation which is derived from a simulating annealing algorithm which is applied to maximize Pragmatic Mutual Information. The algorithm may use a logarithmic, polynomial, or other cooling function. The polynomial cooling function may be particularly appropriate for higher order modulations, such as order 64 and above.

FIGS. 11, 12, 13 and 14 illustrate results indicative of performance of the corresponding signal constellations disclosed herein in Tables 2-3 and FIGS. 9-10, compared to the performance of conventional QAM constellations. These signal constellations were evaluated numerically to obtain the illustrated results. The results were obtained under certain assumptions and are provided by way of example only, and with the understanding that performance may vary in practice.

In FIGS. 11, 12, 13 and 14, the Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR) is illustrated. The illustrated performance is a comparison of eight different conditions, comprising i) constellation 950 (FIG. 10), with Additive White Gaussian Noise (AWGN), phase noise standard deviation (PN STD) of 4; ii) constellation 900 (FIG. 9), with Additive White Gaussian Noise (AWGN), phase noise standard deviation (PN STD) of 7; iii) “Sony”, which is Sony's proposed QAM encoding structure as described in [8]: “IEEE 802.11-15/0601r0, “Non-Uniform Constellations for 64-QAM”” at pages 3-4; iv) “QAM” which refers to conventional rectangular QAM constellation; and v)-viii) correspond to i)-iv), respectively, with Phased Locked Loop (PLL).

FIG. 11 illustrates performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR) for rate 5/8 code, Additive White Gaussian Noise (AWGN), phase noise standard deviation (PN STD) of 4 or 7 (as illustrated), and ideal nonlinearity, Power Spectral Density PSD(0)=−90 dB.

FIG. 12 illustrates performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR) for rate 3/4 code, Additive White Gaussian Noise (AWGN), phase noise standard deviation (PN STD) of 4 or 7 (as illustrated), and ideal nonlinearity, Power Spectral Density PSD(0)=−90 dB.

FIG. 13 illustrates performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR) for rate 13/16 code, Additive White Gaussian Noise (AWGN), phase noise standard deviation (PN STD) of 4 or 7 (as illustrated), and ideal nonlinearity, Power Spectral Density PSD(0)=−90 dB.

FIG. 14 illustrates performance comparison of Frame Error Rate (FER) vs. Peak Signal-To-Noise Ratio (PSNR) for rate 7/8 code, Additive White Gaussian Noise (AWGN), phase noise standard deviation (PN STD) of 4 or 7 (as illustrated), and ideal nonlinearity, Power Spectral Density PSD(0)=−90 dB.

Tables 2-3 as referenced herein are presented below. Table 2 corresponds to constellation 900 illustrated in FIG. 9, and Table 3 corresponds to constellation 950 illustrated in FIG. 10. As noted above, each Table specifies a signal constellation, with each row specifying a constellation symbol in which one of the X and Y values, corresponding to first coordinate values and second coordinate values, respectively, indicates a normalized magnitude of the in-phase component of the constellation symbol and the other of the X and Y values indicates a normalized magnitude of the quadrature component of the constellation symbol. The normalized magnitudes may be scaled. The first column specifies bit sequences corresponding to the constellation symbols. In some embodiments, the entries in the first column can be reordered. In some embodiments, the entries in the second column can be varied, for example by rounding, truncating or varying by up to a predetermined amount.

In some example embodiments, only one quadrant is required, such as the first quadrant. Accordingly, one quarter of the bit sequences and constellations is required. In the example of Tables 2 and 3, only the first 16 out of the 64 bit sequences, and corresponding constellation symbols, would be required. Symmetry operations can be used to account for the remaining quadrants.

TABLE 2 (constellation 900 of FIG. 9): SYMBOL COORDINATE BITS X Y 000000 0.102711 0.503546 000001 0.808833 0.586707 000010 0.292287 0.539416 000011 0.573931 0.511188 000100 0.153478 0.988152 000101 0.478993 0.877326 000110 0.136738 0.766448 000111 0.430209 0.720169 001000 0.101674 0.300318 001001 0.796714 0.173903 001010 0.352378 0.320025 001011 0.585072 0.296273 001100 0.110728 0.096927 001101 0.985272 0.169374 001110 0.321967 0.107949 001111 0.537832 0.093607 010000 0.102711 −0.503546 010001 0.808833 −0.586707 010010 0.292287 −0.539416 010011 0.573931 −0.511188 010100 0.153478 −0.988152 010101 0.478993 −0.877326 010110 0.136738 −0.766448 010111 0.430209 −0.720169 011000 0.101674 −0.300318 011001 0.796714 −0.173903 011010 0.352378 −0.320025 011011 0.585072 −0.296273 011100 0.110728 −0.096927 011101 0.985272 −0.169374 011110 0.321967 −0.107949 011111 0.537832 −0.093607 100000 −0.102711 0.503546 100001 −0.808833 0.586707 100010 −0.292287 0.539416 100011 −0.573931 0.511188 100100 −0.153478 0.988152 100101 −0.478993 0.877326 100110 −0.136738 0.766448 100111 −0.430209 0.720169 101000 −0.101674 0.300318 101001 −0.796714 0.173903 101010 −0.352378 0.320025 101011 −0.585072 0.296273 101100 −0.110728 0.096927 101101 −0.985272 0.169374 101110 −0.321967 0.107949 101111 −0.537832 0.093607 110000 −0.102711 −0.503546 110001 −0.808833 −0.586707 110010 −0.292287 −0.539416 110011 −0.573931 −0.511188 110100 −0.153478 −0.988152 110101 −0.478993 −0.877326 110110 −0.136738 −0.766448 110111 −0.430209 −0.720169 111000 −0.101674 −0.300318 111001 −0.796714 −0.173903 111010 −0.352378 −0.320025 111011 −0.585072 −0.296273 111100 −0.110728 −0.096927 111101 −0.985272 −0.169374 111110 −0.321967 −0.107949 111111 −0.537832 −0.093607

TABLE 3 (constellation 950 of FIG. 10): SYMBOL COORDINATE BITS X Y 000000 0.101262 0.405033 000001 0.713385 0.700766 000010 0.267652 0.512970 000011 0.526309 0.582497 000100 0.131415 0.991327 000101 0.416090 0.909320 000110 0.114535 0.739941 000111 0.356084 0.758285 001000 0.250852 0.180521 001001 0.895785 0.441473 001010 0.425891 0.315992 001011 0.670632 0.370101 001100 0.099375 0.097472 001101 0.986926 0.160648 001110 0.519688 0.099539 001111 0.755082 0.146951 010000 0.101262 −0.405033 010001 0.713385 −0.700766 010010 0.267652 −0.512970 010011 0.526309 −0.582497 010100 0.131415 −0.991327 010101 0.416090 −0.909320 010110 0.114535 −0.739941 010111 0.356084 −0.758285 011000 0.250852 −0.180521 011001 0.895785 −0.441473 011010 0.425891 −0.315992 011011 0.670632 −0.370101 011100 0.099375 −0.097472 011101 0.986926 −0.160648 011110 0.519688 −0.099539 011111 0.755082 −0.146951 100000 −0.101262 0.405033 100001 −0.713385 0.700766 100010 −0.267652 0.512970 100011 −0.526309 0.582497 100100 −0.131415 0.991327 100101 −0.416090 0.909320 100110 −0.114535 0.739941 100111 −0.356084 0.758285 101000 −0.250852 0.180521 101001 −0.895785 0.441473 101010 −0.425891 0.315992 101011 −0.670632 0.370101 101100 −0.099375 0.097472 101101 −0.986926 0.160648 101110 −0.519688 0.099539 101111 −0.755082 0.146951 110000 −0.101262 −0.405033 110001 −0.713385 −0.700766 110010 −0.267652 −0.512970 110011 −0.526309 −0.582497 110100 −0.131415 −0.991327 110101 −0.416090 −0.909320 110110 −0.114535 −0.739941 110111 −0.356084 −0.758285 111000 −0.250852 −0.180521 111001 −0.895785 −0.441473 111010 −0.425891 −0.315992 111011 −0.670632 −0.370101 111100 −0.099375 −0.097472 111101 −0.986926 −0.160648 111110 −0.519688 −0.099539 111111 −0.755082 −0.146951

Through the descriptions of the preceding embodiments, the example embodiments may be implemented by using hardware only or by using software and a necessary universal hardware platform. Based on such understandings, the technical solution of the example embodiments may be embodied in the form of a software product. The software product may be stored in a non-volatile or non-transitory storage medium, which can be a compact disk read-only memory (CD-ROM), USB flash disk, or a removable hard disk. The software product includes a number of instructions that enable a computer device (personal computer, server, or network device) to execute the methods provided in the example embodiments. For example, such an execution may correspond to a simulation of the logical operations as described herein. The software product may additionally or alternatively include number of instructions that enable a computer device to execute operations for configuring or programming a digital logic apparatus in accordance with example embodiments. Example apparatuses and methods described herein, in accordance with example embodiments, can be implemented by one or more controllers. The controllers can comprise hardware, software, or a combination of hardware and software, depending on the particular component and function. In some example embodiments, the one or more controllers can include analog or digital components, and can include one or more processors, one or more non-transitory storage mediums such as memory storing instructions executable by the one or more processors, one or more transceivers (or separate transmitters and receivers), one or more signal processors (analog and/or digital), and/or one or more analog circuit components.

In the described methods or block diagrams, the boxes may represent events, steps, functions, processes, modules, messages, and/or state-based operations, etc. Although some of the above examples have been described as occurring in a particular order, it will be appreciated by persons skilled in the art that some of the steps or processes may be performed in a different order provided that the result of the changed order of any given step will not prevent or impair the occurrence of subsequent steps. Furthermore, some of the messages or steps described above may be removed or combined in other embodiments, and some of the messages or steps described above may be separated into a number of sub-messages or sub-steps in other embodiments. Even further, some or all of the steps may be repeated, as necessary. Elements described as methods or steps similarly apply to systems or subcomponents, and vice-versa. Reference to such words as “sending” or “receiving” could be interchanged depending on the perspective of the particular device. The above discussed embodiments are considered to be illustrative and not restrictive. Example embodiments described as methods would similarly apply to systems, and vice-versa.

Variations may be made to some example embodiments, which may include combinations and sub-combinations of any of the above. The example embodiments presented above are merely examples and are in no way meant to limit the scope of this disclosure. Variations of the innovations described herein will be apparent to persons of ordinary skill in the art, such variations being within the intended scope of the present disclosure. In particular, features from one or more of the above-described embodiments may be selected to create alternative embodiments comprised of a sub-combination of features which may not be explicitly described above. In addition, features from one or more of the above-described embodiments may be selected and combined to create alternative embodiments comprised of a combination of features which may not be explicitly described above. Features suitable for such combinations and sub-combinations would be readily apparent to persons skilled in the art upon review of the present disclosure as a whole. The subject matter described herein intends to cover and embrace all suitable changes in technology.

The specification and drawings are, accordingly, to be regarded simply as an illustration, and are contemplated to cover any and all modifications, variations, combinations or equivalents.

The following are references that are incorporated herein by reference in their entirety:

-   [1] T. Hwang, C. Yang, G. Wu, S. Li, and G. Y. Li, “OFDM and its     wireless applications: A survey,” IEEE Trans. Veh. Technol., vol.     58, no. 4, pp. 1673-1694, May 2009. -   [2] H. Sari, G. Karam, and I. Jeanclaude, “Frequency-domain     equalization of mobile radio and terrestrial broadcast channels,” in     Proc. Conf. Global Commun. (GLOBECOM), San Francisco, Calif.,     November/December 1994, pp. 1-5. -   [3] IEEE P802.11-REVmc/D2.4: Wireless LAN Medium Access Control     (MAC) and Physical Layer (PHY) Specifications. -   [4] IEEE Std 802.11-2016. -   [5] ETSI EN 302 307-2: Digital Video Broadcast; Part 2: DVB-S2     extensions (DVB-S2X). -   [6] IEEE 802.11-14/1154r8, “802.11 NG60 SG Proposed PAR”. -   [7] IEEE 802.11-15/0339r0, “SC 64APSK for 802.11ay”. -   [8] IEEE 802.11-15/0601r0, “Non-Uniform Constellations for 64-QAM”. -   [9] PCT/CN2016/078101, “High Order Modulations for Single Carrier     Transmission”, filed on Mar. 31, 2016. -   [10] IEEE 802.11-09/0296r16, “TGad Evaluation Methodology”. -   [11] F. Kayhan and G. Montorsi, “Joint signal-labeling optimization     under peak power constraint,” International Journal of Satellite     Communications and Networking, 2012. -   [12] F. Kayhan and G. Montorsi. “Constellation design for     transmission over nonlinear satellite channels.” Global     Communications Conference (GLOBECOM), 2012, IEEE 2012. -   [13] F. Kayhan and G. Montorsi. “Constellation design for channels     affected by phase noise.” Communications (ICC), 2013 IEEE     International Conference on. IEEE, 2013. 

What is claimed is:
 1. A method for wireless communication using digital Quadrature Amplitude Modulation (QAM), the method comprising: demodulating, using a controller of a wireless communication device, a signal in accordance with a 64-point constellation, the signal being for transmission or detected in a received signal, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.102711 0.503546 0.808833 0.586707 0.292287 0.539416 0.573931 0.511188 0.153478 0.988152 0.478993 0.877326 0.136738 0.766448 0.430209 0.720169 0.101674 0.300318 0.796714 0.173903 0.352378 0.320025 0.585072 0.296273 0.110728 0.096927 0.985272 0.169374 0.321967 0.107949 0.537832 0.093607.


2. The method of claim 1, wherein normalized magnitudes of the constellation symbols in the first quadrant of the 64-point constellation are defined by the coordinate pairs to at least four decimal places of precision.
 3. The method of claim 1, wherein normalized magnitudes of the constellation symbols in the first quadrant of the 64-point constellation are defined by the coordinate pairs to at least five decimal places of precision.
 4. The method of claim 1, wherein normalized magnitudes of the constellation symbols in the first quadrant of the 64-point constellation are defined by the coordinate pairs to six decimal places of precision.
 5. The method of claim 1, wherein the 64-point constellation is a reflection-symmetric constellation.
 6. The method of claim 1, wherein: the first coordinates of the coordinate pairs represent normalized magnitudes of one of: in-phase components and quadrature components of the constellation symbols, and the second coordinates of the coordinate pairs represent normalized magnitudes of the other one of the in-phase components and the quadrature components of the constellation symbols.
 7. The method of claim 1, wherein the demodulated signal includes bit sequences, and the bit sequences are assigned to the constellation symbols using Gray mapping.
 8. The method of claim 1, wherein the demodulated signal includes bit sequences, and each of the bit sequences is of length 6 bits, including 4 quadrant non-specific bits, and wherein, for an index value k ranging from k=1 to k=16 inclusive: the quadrant non-specific bits of the bit sequence corresponding to the constellation symbol defined by a k^(th)-listed one of the coordinate pairs are equal to: a binary representation of k−1; the binary representation of k−1 added to a constant value under Modulo-16 addition; the binary representation of k−1 subjected to a consistent bit reordering, or the binary representation of k−1 added to a constant value under Modulo-16 addition and subjected to the consistent bit reordering.
 9. The method of claim 8, wherein the 64-point constellation is a reflection symmetric constellation, and wherein bit sequences corresponding to constellation symbols within a common group of reflection symmetric constellation symbols have identical quadrant non-specific bits.
 10. The method of claim 1, wherein the controller comprises a mapping module electronic component for said demodulating.
 11. An apparatus for a wireless communication device configured for wireless communication using digital Quadrature Amplitude Modulation (QAM), the apparatus comprising: a controller configured to demodulate a signal in accordance with a 64-point constellation, the signal being for transmission or detected in a received signal, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.102711 0.503546 0.808833 0.586707 0.292287 0.539416 0.573931 0.511188 0.153478 0.988152 0.478993 0.877326 0.136738 0.766448 0.430209 0.720169 0.101674 0.300318 0.796714 0.173903 0.352378 0.320025 0.585072 0.296273 0.110728 0.096927 0.985272 0.169374 0.321967 0.107949 0.537832 0.093607.


12. The apparatus of claim 11, wherein normalized magnitudes of the constellation symbols in the first quadrant of the 64-point constellation are defined by the coordinate pairs to at least four decimal places of precision.
 13. The apparatus of claim 11, wherein normalized magnitudes of the constellation symbols in the first quadrant of the 64-point constellation are defined by the coordinate pairs to at least five decimal places of precision.
 14. The apparatus of claim 11, wherein normalized magnitudes of the constellation symbols in the first quadrant of the 64-point constellation are defined by the coordinate pairs to six decimal places of precision.
 15. The apparatus of claim 11, wherein the 64-point constellation is a reflection-symmetric constellation.
 16. The apparatus of claim 11, wherein the first coordinates of the coordinate pairs represent normalized magnitudes of one of: in-phase components and quadrature components of the constellation symbols, and the second coordinates of the coordinate pairs represent normalized magnitudes of the other one of the in-phase components and the quadrature components of the constellation symbols.
 17. The apparatus of claim 11, wherein the demodulated signal includes bit sequences, and the bit sequences are assigned to the constellation symbols using Gray mapping.
 18. The apparatus of claim 11, wherein the demodulated signal includes bit sequences, and each of the bit sequences is of length 6 bits, including 4 quadrant non-specific bits, and wherein, for an index value k ranging from k=1 to k=16 inclusive: the quadrant non-specific bits of the bit sequence corresponding to the constellation symbol defined by a k^(th)-listed one of the coordinate pairs are equal to: a binary representation of k−1; the binary representation of k−1 added to a constant value under Modulo-16 addition; the binary representation of k−1 subjected to a consistent bit reordering, or the binary representation of k−1 added to a constant value under Modulo-16 addition and subjected to the consistent bit reordering.
 19. The apparatus of claim 18, wherein the signal constellation is a reflection symmetric constellation, and wherein bit sequences corresponding to constellation symbols within a common group of reflection symmetric constellation symbols have identical quadrant non-specific bits.
 20. The apparatus of claim 11, wherein the controller comprises a mapping module electronic component for said demodulating.
 21. A non-transitory computer readable medium containing instructions for wireless communication using digital Quadrature Amplitude Modulation (QAM), the non-transitory computer readable medium comprising instructions executable by a controller of a wireless communication device, the instructions comprising: instructions for demodulating a signal in accordance with a 64-point constellation, the signal being for transmission or detected in a received signal, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.102711 0.503546 0.808833 0.586707 0.292287 0.539416 0.573931 0.511188 0.153478 0.988152 0.478993 0.877326 0.136738 0.766448 0.430209 0.720169 0.101674 0.300318 0.796714 0.173903 0.352378 0.320025 0.585072 0.296273 0.110728 0.096927 0.985272 0.169374 0.321967 0.107949 0.537832 0.093607.


22. A method for wireless communication using digital Quadrature Amplitude Modulation (QAM), the method comprising: demodulating, using a controller of a wireless communication device, a signal in accordance with a 64-point constellation, the signal being for transmission or detected in a received signal, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.101262 0.405033 0.713385 0.700766 0.267652 0.512970 0.526309 0.582497 0.131415 0.991327 0.416090 0.909320 0.114535 0.739941 0.356084 0.758285 0.250852 0.180521 0.895785 0.441473 0.425891 0.315992 0.670632 0.370101 0.099375 0.097472 0.986926 0.160648 0.519688 0.099539 0.755082 0.146951.


23. An apparatus for a wireless communication device configured for wireless communication using digital Quadrature Amplitude Modulation (QAM), the apparatus comprising: a controller configured to demodulate a signal in accordance with a 64-point constellation, the signal being for transmission or detected in a received signal, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.101262 0.405033 0.713385 0.700766 0.267652 0.512970 0.526309 0.582497 0.131415 0.991327 0.416090 0.909320 0.114535 0.739941 0.356084 0.758285 0.250852 0.180521 0.895785 0.441473 0.425891 0.315992 0.670632 0.370101 0.099375 0.097472 0.986926 0.160648 0.519688 0.099539 0.755082 0.146951.


24. A non-transitory computer readable medium containing instructions for wireless communication using digital Quadrature Amplitude Modulation (QAM), the non-transitory computer readable medium comprising instructions executable by a controller of a wireless communication device, the instructions comprising: instructions for demodulating a signal in accordance with a 64-point constellation, the signal being for transmission or detected in a received signal, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.101262 0.405033 0.713385 0.700766 0.267652 0.512970 0.526309 0.582497 0.131415 0.991327 0.416090 0.909320 0.114535 0.739941 0.356084 0.758285 0.250852 0.180521 0.895785 0.441473 0.425891 0.315992 0.670632 0.370101 0.099375 0.097472 0.986926 0.160648 0.519688 0.099539 0.755082 0.146951.


25. A method for wireless communication using digital Quadrature Amplitude Modulation (QAM), the method comprising: modulating, using a controller of a wireless communication device, a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received; wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.102711 0.503546 0.808833 0.586707 0.292287 0.539416 0.573931 0.511188 0.153478 0.988152 0.478993 0.877326 0.136738 0.766448 0.430209 0.720169 0.101674 0.300318 0.796714 0.173903 0.352378 0.320025 0.585072 0.296273 0.110728 0.096927 0.985272 0.169374 0.321967 0.107949 0.537832 0.093607.


26. An apparatus for a wireless communication device configured for wireless communication using digital Quadrature Amplitude Modulation (QAM), the apparatus comprising: a controller configured to modulate a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.102711 0.503546 0.808833 0.586707 0.292287 0.539416 0.573931 0.511188 0.153478 0.988152 0.478993 0.877326 0.136738 0.766448 0.430209 0.720169 0.101674 0.300318 0.796714 0.173903 0.352378 0.320025 0.585072 0.296273 0.110728 0.096927 0.985272 0.169374 0.321967 0.107949 0.537832 0.093607.


27. A non-transitory computer readable medium containing instructions for wireless communication using digital Quadrature Amplitude Modulation (QAM), the non-transitory computer readable medium comprising instructions executable by a controller of a wireless communication device, the instructions comprising: instructions for modulating a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received; wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.102711 0.503546 0.808833 0.586707 0.292287 0.539416 0.573931 0.511188 0.153478 0.988152 0.478993 0.877326 0.136738 0.766448 0.430209 0.720169 0.101674 0.300318 0.796714 0.173903 0.352378 0.320025 0.585072 0.296273 0.110728 0.096927 0.985272 0.169374 0.321967 0.107949 0.537832 0.093607.


28. A method for wireless communication using digital Quadrature Amplitude Modulation (QAM), the method comprising: modulating, using a controller of a wireless communication device, a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received; wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.101262 0.405033 0.713385 0.700766 0.267652 0.512970 0.526309 0.582497 0.131415 0.991327 0.416090 0.909320 0.114535 0.739941 0.356084 0.758285 0.250852 0.180521 0.895785 0.441473 0.425891 0.315992 0.670632 0.370101 0.099375 0.097472 0.986926 0.160648 0.519688 0.099539 0.755082 0.146951.


29. An apparatus for a wireless communication device configured for wireless communication using digital Quadrature Amplitude Modulation (QAM), the apparatus comprising: a controller configured to modulate a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received, wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.101262 0.405033 0.713385 0.700766 0.267652 0.512970 0.526309 0.582497 0.131415 0.991327 0.416090 0.909320 0.114535 0.739941 0.356084 0.758285 0.250852 0.180521 0.895785 0.441473 0.425891 0.315992 0.670632 0.370101 0.099375 0.097472 0.986926 0.160648 0.519688 0.099539 0.755082 0.146951.


30. A non-transitory computer readable medium containing instructions for wireless communication using digital Quadrature Amplitude Modulation (QAM), the non-transitory computer readable medium comprising instructions executable by a controller of a wireless communication device, the instructions comprising: instructions for modulating a signal in accordance with a 64-point constellation, the signal being for transmission or the signal being received; wherein normalized magnitudes of constellation symbols in a first quadrant of the 64-point constellation are defined by the following coordinate pairs to at least three decimal places of precision: first coordinate second coordinate 0.101262 0.405033 0.713385 0.700766 0.267652 0.512970 0.526309 0.582497 0.131415 0.991327 0.416090 0.909320 0.114535 0.739941 0.356084 0.758285 0.250852 0.180521 0.895785 0.441473 0.425891 0.315992 0.670632 0.370101 0.099375 0.097472 0.986926 0.160648 0.519688 0.099539 0.755082 0.146951. 